Ask The Wizard #151
Soft 18 Vs Ace Combinatorial Analysis
Explanation of column titles
Player cards:Cards in player’s hand
Conditional probability: Given that the player has a soft 18 against a dealer ace the probability of the given hand composition.
Hit EV:Expected value by hitting
Stand EV:Expected value by standing
Hit Return:Product of probability and hit expected value
Stand Return:Product of probability and stand expected value
The right two cells of the bottom row show that overall the expected value of hitting is -0.105807 and for standing is -0.102375. So, the table shows the odds favor standing by 0.00343.
To confirm these results I ran two simulations under the rules in question, one simulation hitting and one standing on this play. I counted only hands where soft 18 against a dealer ace happened at any time during play. Here are my results.
Soft 18 Vs Ace Simulation
So, the simulation shows the odds favor standing by 0.0025 over all possible scenarios where this hand turns up. Thus, for practical purposes of playing all hands, the best play is to stand, contrary to what my basic strategy chart says.
- 50 St. James, London, England
- Atalantis at Paradise Island, Nassau, Bahamas
- Casino Baden-Baden, Germany
- Casino Bellevue Marienbad, Czech Republic
- Casino de Montreal, Montreal Quebec
- Le Casino, Monte Carlo
- St. James Club, Antigua
- Taleon Club, Saint Petersburg, Russia
- Venetian, Las Vegas, Nevada
1=0.97434 + j*(0.024686/940)
j = (1-0.97434)/(0.024686/940) = 977.33182.
So the breakeven point is a meter of 977.33 bet units or $4886.66. This assumes perfect 940/9/6 strategy. However few people know 940/9/6 strategy. If using 800/9/6 strategy then we would use the 800/9/6 table:
1 = (0.99543904-0.01980661) + j*(0.01980661/800)
j = (1 - (0.99543904-0.01980661))/(0.01980661/800)
j = 984.2197
So if using 800/9/6 strategy the jackpot would need to reach 984.22 bet units or $4921.10.
0.01% Losing Percentile in Blackjack
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